A lattice-theoretical morphological view on template extraction in images

The extraction of copies of a template appearing in a figure can be defined as the composition of a hit-or-miss transform by a pair of structuring elements, followed by a dilation by the first structuring element. On the other hand, the operation of template extraction can be abstractly characterized by the three requirements of antiextensivity, idempotence, and a new property that we call ''overcondensation''; we designate by ''open-overcondensation'' an operator having these three properties. Examples include digital contour extraction, or the above-mentioned composition of a hit-or-miss transform by a dilation, Decompositions formulas of open-overcondensations in terms of such operators are given; they parallel the well-known decomposition formulas for openings. Generalizations of ''rank-max'' openings and inf-overfilters are also given. These results hold not only for sets or gray-level images, they are valid in the framework of complete lattices. (C) 1996 Academic Press, Inc.